Random Sampling and

Introduction to Experimental Design

Simple Random Sample:

• n measurements from a population • Population subset• Selected such that:– Every sample of size n from the population has an

equal chance of being selected– Every member of the population has an equal

chance of being included

How to select a simple random sample:

• Assign an number to each child.• Use Random Number Table A13• Pick the first 5 two digit numbers.

Example

Simulation:

• Provides arithmetic imitations of “real” situations.

• Stock Exchange Problem.

Sampling with replacement:Item selected for a sample is not removed

Other Sampling Techniques

Stratified Sampling:• Groups or classes inside a population that share

common characteristics (strata). A random sample is drawn for each strata.

Systematic Sampling:• Elements of a population are in some order,

then you select a starting point and every kth element for sampling

Other Sampling Techniques:

Cluster Sampling:• A demographic region is divided into sections.

Then you randomly select sections or clusters and every member is included in the sampling

Convenience Sampling:• Results or data that is conveniently and

readably obtained

Introduction to a Statistical Study• Basic guidelines for planning a statistical study• Identify the individuals or objects of interest• Specify the variables as well as protocols for taking measurements or

making observations• Determine if you will use an entire population (use a census) or a

representation sample. If using a sample, decide on a viable sampling method

• Collect data.• Use appropriate descriptive statistics methods (chapters 2, 3, 10) and

make decisions using appropriate inferential statistics (chapters 8-12)• Note an concerns you might have about your data collection methods

and list any recommendations for future studies

Observation or Experiment?

Observational Study: • An activity when the experimenter notes

differences and their effects on the measurement

Experiment:• A planned activity that results in measurements.• Treatment is deliberately imposed on the individual

in order to observe change in the variable.

Planning and Conducting Experiments

Response/Dependent Variable:• Variable to be measured in the experiment

Explanatory/Independent Variable:• Variable that may explain the differences in responses

Control:• Used to establish the baseline response expected if

no treatment is given

Planning and Conducting Experiments

Placebo:• A control group for some medical experiments• Looks exactly like the real medicine

Randomized two-treatment experiment:• Patients assigned to the treatment and control

group by random selection

Planning and Conducting Experiments

Single-Blind:• Either the patient does not know which treatment

he/she is receiving or the person measuring the patient’s reaction does not know

Double-Blind:• Both the patient and the person measuring do not

know which treatment the patient was given

Survey

Nonresponse:• Selected respondents refuse to respond• Too many nonresponses can cause the study to be biased

Voluntary Response:• Often over represents people with strong opinions

Hidden Bias:• The way you conduct the survey many leave part of a

population out

Results

Lurking/Confounding Variable:• The effect of one variable on another can be

hidden by other variables for which no data has been obtained

Generalizing results:• Replication